{"id":"hexagon/2611.00073","pdf":"https://hexagonmath.org/pdf/2611.00073v1","url":"https://hexagonmath.org/abs/2611.00073v1","tags":["msc:11G05","msc:11G18","msc:14G05","Elliptic Curves","Number fields","modular curves","sporadic points","torsion"],"score":0,"title":"Torsion of elliptic curves over number fields of degree $6$, $7$, $8$ and $9$","domain":"math.NT","origin":"ai-generated","source":"hexagon","authors":["Filip Najman"],"reviews":0,"subject":"math.NT","summary":"We determine all the groups that appear as the torsion group of an elliptic curve over a number field of degree $d$ for $d=6$, $7$, $8$ and $9$. Apart from the groups that occur infinitely often, exactly $4$ groups occur in degree $6$, $3$ in degree $7$, $8$ in degree $8$ and $9$ in degree $9$, and among them the groups $\\mathbb{Z}/2\\mathbb{Z}\\times\\mathbb{Z}/24\\mathbb{Z}$ over sextic fields, $\\mathbb{Z}/3\\mathbb{Z}\\times\\mathbb{Z}/15\\mathbb{Z}$ over octic fields and $\\mathbb{Z}/2\\mathbb{Z}\\times\\mathbb{Z}/26\\mathbb{Z}$ over nonic fields were not known to occur. For $13$ of these $24$ pairs…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["ChatGPT","Claude Opus","Magma"],"discussed":0,"published":"2026-11-04","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}